Using neural networks to deduce polymer molecular weight distributions from linear rheology

We present a methodology for inferring the molecular weight distribution (MWD) of polydisperse linear polymers from their linear rheology using machine learning techniques. Specifically, we use a state-of-the-art tube model to generate large datasets of artificially produced rheology data. These are used to train neural networks (NNs) to make accurate MWD predictions from frequency-sweep rheology measurements. We target distributions relevant to commercial polymers, so broad polydisperse MWDs are prioritized. To simplify the data format for the NN, we fit Maxwell modes to the rheology with predefined relaxation times and, hence, parameterize the rheology using the mode amplitudes; correspondingly, we propose MWD parameterization using the sum of several log-Gaussian subdistributions with logarithmically spaced mean molecular weights and identical dispersities. We assess the methodology’s performance by predicting MWDs using experimental polystyrene rheology data from the literature. Good agreement with gel permeation chromatography data is found where available, and where it is not, the prediction captures known molecular weight statistics (such as weight-average molecular weight and dispersity) even if the precise shape of the MWD is not known. The findings here lay the groundwork for future developments concerning the inversion of this tube model for other polymeric materials. The ability to infer the MWD from rheology would traditionally be prohibited by the mathematical complexity of state-of-the-art tube models, but we bypass this issue with our machine learning methodology.